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Coherent orthogonal binary FSK modulation is used to transmit two equiprobable symbol waveforms $s_{1}( t )= \alpha \cos 2\pi f_1 t$, and $s_2(t)  = \alpha \cos 2 \pi f_2 t$ where $\alpha = 4$ mV. Assume an AWGN channel with two-sided noise power spectral density $\frac{N_o}{2}= 0.5 \times 10^{-12}$ W/Hz. Using an optimal receiver and the relation $Q(v)= \frac{1}{\sqrt{2\pi }}\int ^{\infty }_{v} e^{-u^2/2} \: du,$ the bit error probability for a data rate of $500$ kbps is

  1. $Q(2)$
  2. $Q(2\sqrt{2})$
  3. $Q(4)$
  4. $Q(4\sqrt{2})$
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